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Three-term commutator
estimates and the regularity of
 -harmonic maps into
spheres
Francesca Da Lio and Tristan Rivière |
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Vol. 4 (2011), No. 1, 149–190
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Abstract |
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We prove the regularity of weak -harmonic maps from the real line into a sphere. A key step is the formulation of the -harmonic map equation in the form of a nonlocal linear Schrödinger type equation with three-term commutators on the right-hand side. We then establish a sharp estimate for these three-term commutators. |
Keywords
harmonic map, nonlinear elliptic PDE, regularity of
solutions, commutator estimates
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Mathematical Subject Classification 2000
Primary: 58E20, 35B65, 35J20, 35J60, 35S99
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Milestones
Received: 23 July 2009
Accepted: 10 March 2010
Published: 27 March 2011
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Authors |
| Francesca Da Lio | |
| Dipartimento di Matematica Pura ed
Applicata Università degli Studi di Padova Via Trieste 63 35121 Padova Italy |
Department of Mathematics ETH Zürich Rämistrasse 101 8092 Zürich Switzerland |
| Tristan Rivière | |
| Department of Mathematics ETH Zürich Rämistrasse 101 8092 Zürich Switzerland |
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| http://www.math.ethz.ch/~riviere/ | |
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